Apps have unique IDs like com.liftoffapp.liftoff and f-droid/play store don’t know who installed an app. They just show you all installed apps that are in their repos and look for updates for them. If they wouldn’t handle it like that, you wouldn’t get any updates if you installed an .apk manually. If an .apk gets installed and there is already an app with that ID, it replaces it and that’s how updates work. So if they both do an update, the first update will replace the old version and the second update will replace the first.

In the past apps from play store and from official f-droid repo wouldn’t replace each other without further user confirmation and deletion of user data. I don’t know if it’s still handled like that. F-Droid builds and signs packages on it’s own, which results in a signature key mismatch. It’s different for repos like IzzyOnDroid which just distribute official builds and therefore are signed with the same key. Though IzzyOnDroid has a key mismatch with F-Droid.

Usually a different key means that somebody modified the app and you don’t want an malicious app to be blindly installed or have access to the app’s user data. But F-Droid have no other choice when they build the packages themselves.